# Quantitative Methods for Business Cha 2—Introduction to Probability PROBLEM

PROBLEM

1. A market study taken at a local sporting goods store showed that of 20 people questioned, 6 owned tents, 10 owned sleeping bags, 8 owned camping stoves, 4 owned both tents and camping stoves, and 4 owned both sleeping bags and camping stoves.

Let:

Event A = owns a tent

Event B = owns a sleeping bag

Event C = owns a camping stove

and let the sample space be the 20 people questioned.

a.

Find P(A), P(B), P(C), P(A C), P(B C).

b.

Are the events A and C mutually exclusive? Explain briefly.

c.

Are the events B and C independent events? Explain briefly.

d.

If a person questioned owns a tent, what is the probability he also owns a camping stove?

e.

If two people

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.2177

10. A corporation has 15,000 employees. Sixty-two percent of the employees are male. Twenty-three percent of the employees earn more than $30,000 a year. Eighteen percent of the employees are male and earn more than $30,000 a year.

a.

If an employee is taken at random, what is the probability that the employee is male?

b.

If an employee is taken at random, what is the probability that the employee earns more than $30,000 a year?

c.

If an employee is taken at random, what is the probability that the employee is male and earns more than $30,000 a year?

d.

If an employee is taken at random, what is the probability that the employee is male or earns more than $30,000 a year or both?

e.

The employee taken at random turns out to be male. Compute the probability that he earns more than $30,000 a year.

f.

Are being male and earning more than $30,000 a year independent?

ANSWER:

a.

0.62

b.

0.23

c.

0.18

d.

0.67

e.

0.2903

f.

No

Chapter 3—Probability Distributions

1. Delicious Candy markets a two pound box of assorted chocolates. Because of imperfections in the candy making equipment, the actual weight of the chocolate has a continuous uniform distribution ranging from 31.8 to 32.6 ounces.

a.

Define a probability density function for the weight of the box of chocolate.

b.

What is the probability that a box weighs (1) exactly 32 ounces; (2) more than 32.3 ounces; (3) less